Continuous rotation in AN with certain control behavior? (Speed)
To be able to properly animate in Blender, it is important that frames can be evaluated indepedently without the need for a previous frame or start frame. (Sometimes you want to change the start frame, but frame X should still show the same content.)

Create an empty object, which controls the speed. I added and empty circle and keyframed its X-axis. Grab that Fcurve with Animation nodes.

The position on a frame is merely the accumulation of the speed-value on all previous frames.

To simplify the matter


I use a starting position of 0
interpret the input speed value [from the fcurve] as speed per frame
ignore the subframes (no differential equations) and pretend the speed to be constant for the duration of a frame


but you can easily add the first and second bullet points.

This means we have to get a list of speed values up to the current frame. For that, I use a loop with as many iterations as the current frame number and evaluate the speed-fcurve's value. The resulting list must be summed to get the actual value. I use it to control the X position of a cuboid.

With movement on multiple axis this actually the same.





Final note, do not go the math routes. Although I don't know your context, integrals are most likely overkill.